ASYMPTOTIC-BEHAVIOR OF SAMPLE-MEAN DIRECTION FOR SPHERES

In this note we consider some asymptotic properties of empirical mean direction on spheres. We do not require any symmetry for the underlyin g density. Thus our results provide the framework for an asymptotic in ference regarding mean direction under very weak model assumptions. Me an direction is a specialization of the more general concept of mean l ocation applicable to arbitrary (compact) submanifolds of Euclidean sp ace, to which the methods of this paper could be applied. (C) 1996 Aca demic Press, Inc.